and radius 
.
.
complex numbers with 
such that
Find the value of 
.
.
Let 
.
and 
be complex numbers. For a complex number 
where 
,
to be the distance of 
from the origin, or 
.
be the minimum value and 
be the maximum value of 
for all complex numbers 
.
.
such that,
From here we must have,
Observe that thus far the RHS of the divisibility statement has been strictly positive, following from the fact that 
for 
.
to be,
,
.
.
be 
,
.
?
through 
,
such that 
is also prime.
vertices of an octagon each red, black, and white, such that no two adjacent sides are the same color?
be the number of positive integers 
and 
divides
where 
denotes the number of positive integers that divide 
.
Y by bjump
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What is my chance to make USAMO 2025 with a 100.5 on AMC 12A?
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Hi everyone, I got a 100.5 on AMC 12A 2024 what is my chance to make USAMO 2025? (i did not do 12B btw)
